A381967 Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, the factorial base expansion of n*a(n) only contains distinct nonzero digits.

0, 1, 2, 4, 3, 10, 6, 7, 9, 8, 5, 12, 11, 18, 14, 16, 15, 22, 13, 19, 23, 24, 17, 20, 21, 26, 25, 40, 39, 42, 32, 54, 30, 36, 48, 62, 33, 61, 51, 28, 27, 53, 29, 67, 49, 64, 47, 46, 34, 44, 58, 38, 55, 41, 31, 52, 57, 56, 50, 59, 60, 37, 35, 66, 45, 68, 63, 43

Offset: 0

Author

Rémy Sigrist, Mar 12 2025

Keywords

• nonn
• base

Comments

This sequence is a self-inverse permutation of the nonnegative integers.

This sequence is well defined: for any n > 0 and k > n, the factorial base expansion of k!, a multiple of n, contains distinct nonzero digits (in fact: a single 1 digit).

Examples

			The first terms, alongside the factorial base expansion of n*a(n), are:
  n   a(n)  fact(n*a(n))
  --  ----  ------------
   0     0  0
   1     1  1
   2     2  2,0
   3     4  2,0,0
   4     3  2,0,0
   5    10  2,0,1,0
   6     6  1,2,0,0
   7     7  2,0,0,1
   8     9  3,0,0,0
   9     8  3,0,0,0
  10     5  2,0,1,0
  11    12  1,0,2,0,0
  12    11  1,0,2,0,0
  13    18  1,4,3,0,0
  14    14  1,3,0,2,0
  15    16  2,0,0,0,0
  16    15  2,0,0,0,0
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..10000
• Rémy Sigrist, Scatterplot of the first 50000 terms
• Rémy Sigrist, PARI program
• Index entries for sequences related to factorial base representation
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A265349.

Programs

PARI

\\ See Links section.